The stealth characteristics of the Zumwalt class give it the radar characteristics of a fishing boat. It is not invisible, but it can cast doubt as to what it is if it is operating on its own, and it likely has a somewhat shorter detection range. The idea is it might be able to approuch a coastline and fire its missiles or guns to take out defenses before the enemy can figure out what is going.
As for the individual cost, that comes down the very limited run. The Navy wanted to kill the program once they decided the design goals were not what they need, and instead wanted to build more Burkes. Congress ordered them to keep the program going with three ships instead of the original 20 or so.
One of the good things to come from the program is the electrical system. Instead of shaft driven propellers, each propeller has a motor linked to the generators by wire. The Zumwalt produces an unusually large amount of power, not just to run its radar, but also also with railguns and lasers in mind. The third Zumwalt class ship will have at least one 64 megawatt rail gun in the second turret, and keep the 155 mm AGS (advanced gun system) in the lead turret.
Getting the Burke class firing rail guns without a major overhaul is not going to happen, even the radar upgrade had to be scaled back due to power limitations. Defensive lasers will work, because they do not have to be particularly power intensive. There are several proposals for upgrading the Burke, none of which are ideal. It should probably come down to a new design but with the Burke's role of fleet defense firmly in mind.
